Modern cliche about getting 80% of the content for 20% of the effort. Also known as "the Pareto Principle".
Benjamin Geiger: This is much more widely found than it may appear.
Software engineers know it as "20% of the code leads to 80% of the effort/bugs". Retailers know it as "20% of customers generate 80% of sales" or "80% of merchandise comes from 20% of vendors". I guess that go players might agree that 80% of thickness or territory comes from 20% of the moves...
Bill: And then there is the Gates Principle: "It all belongs to me." ;-)[1]
Seriously, if the size of go plays decreases linearly, we get this kind of picture:
|\ | \ | \ | \ Value | \ | |\ | 80 | \ | | \ | |20 \ ------------- 0 .55 P P Plays
In that case, about 55% of the plays produce 80% of the territory.
My impression is that the curve is flatter on both ends, with large plays predominating before the endgame, followed by a rather quick drop to smaller plays. Then you have maybe 65% of the plays producing 80% of the territory.
Evpsych: The territory? Do you mean unclaimed? Undefended? Uninvadable?
At move 1, how much territory is claimed? X=komi? The whole board? Some inscrutable CGT temperature/pressure/quantum entanglement measure? :)
If there is a capture, was that a refuted claim? Is it a land rush? A battle for grabbing the other's territory?
I'm trying to figure out what you mean by territory, as simple as that sounds! Thanks for any clarification...
Charles Matthews Suppose you have a game in which in the middle game the exchange of a few plays Black/White/Black/.../White does not leave the current scores about where they were. Then the game will look like a mismatch, assuming the swing in the score is always one way. That's how games go when the players are half-a-dozen stones apart in level. So the straight line graph is a reasonable evened-out model for well-played games at higher handicaps, where White catches up gradually. For even games, you might instead expect a flat portion in a graph based on positional judgement, from about move 50 to 150. Various exchanges occur in the amounts of territory sketched out in the opening, with framework -> influence -> territory being a natural process.
I think what Bill may be hypothesising is about consolidation of territory: the split (for one player) in positional judgement between solid territory and influence ends up as 100% territory at the end of the game, and one could graph the derivative of the territory component.
Bill: To answer Evpsych's question, Benjamin started off talking about "thickness or territory". I took him to mean value in a general sense, not specifying which form it takes. I just said "territory", since thickness is eventualy translated into territory. I labeled one dimension of my graph, "value". By "territory" I meant the net value of a whole board position.
At the end of the game each player may have around 60 points, for instance. However, each player has gained more than a dozen times that. Most such gains have been countered by plays that nearly erased them, so the actual territory at the end of the game is a mere fraction of the gains made during play.
Perhaps Benjamin was thinking about the plays that finally consolidate territory or thickness. Indeed, there are very few of those. Sometimes they are huge plays, but for the most part they are relatively unimportant. Oba do not make territory yet, but they add much value to your position. They, and other large plays, are what this saying should be about. To use the business metaphor, we give credit to the salesman who makes the sale, not the cashier who takes the money.
[1] Or Cho Chikun, according to give up some territory.